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Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic…

Machine Learning · Computer Science 2022-05-27 Benedek Rozemberczki , Lauren Watson , Péter Bayer , Hao-Tsung Yang , Olivér Kiss , Sebastian Nilsson , Rik Sarkar

Cooperative game theory methods, notably Shapley values, have significantly enhanced machine learning (ML) interpretability. However, existing explainable AI (XAI) frameworks mainly attribute average model predictions, overlooking…

Artificial Intelligence · Computer Science 2025-05-20 Marouane Il Idrissi , Agathe Fernandes Machado , Ewen Gallic , Arthur Charpentier

While Explainable Artificial Intelligence (XAI) is increasingly expanding more areas of application, little has been applied to make deep Reinforcement Learning (RL) more comprehensible. As RL becomes ubiquitous and used in critical and…

Artificial Intelligence · Computer Science 2021-10-05 Alexandre Heuillet , Fabien Couthouis , Natalia Díaz-Rodríguez

The Shapley value has become popular in the Explainable AI (XAI) literature, thanks, to a large extent, to a solid theoretical foundation, including four "favourable and fair" axioms for attribution in transferable utility games. The…

Machine Learning · Computer Science 2021-02-23 Daniel Fryer , Inga Strümke , Hien Nguyen

This work focuses on developing efficient post-hoc explanations for quantum AI algorithms. In classical contexts, the cooperative game theory concept of the Shapley value adapts naturally to post-hoc explanations, where it can be used to…

Quantum Physics · Physics 2025-04-18 Iain Burge , Michel Barbeau , Joaquin Garcia-Alfaro

In many multi-agent settings, participants can form teams to achieve collective outcomes that may far surpass their individual capabilities. Measuring the relative contributions of agents and allocating them shares of the reward that…

Machine Learning · Computer Science 2022-08-19 Daphne Cornelisse , Thomas Rood , Mateusz Malinowski , Yoram Bachrach , Tal Kachman

A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game…

Machine Learning · Computer Science 2020-06-29 Luke Merrick , Ankur Taly

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements…

Artificial Intelligence · Computer Science 2020-07-01 I. Elizabeth Kumar , Suresh Venkatasubramanian , Carlos Scheidegger , Sorelle Friedler

Additive feature explanations using Shapley values have become popular for providing transparency into the relative importance of each feature to an individual prediction of a machine learning model. While Shapley values provide a unique…

Machine Learning · Computer Science 2021-12-21 Thomas W. Campbell , Heinrich Roder , Robert W. Georgantas , Joanna Roder

Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…

Theoretical Economics · Economics 2019-05-13 Jacob North Clark , Stephen Montgomery-Smith

Feature attribution methods help make machine learning-based inference explainable by determining how much one or several features have contributed to a model's output. A particularly popular attribution method is based on the Shapley value…

Artificial Intelligence · Computer Science 2025-11-04 Filip Naudot , Tobias Sundqvist , Timotheus Kampik

As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory,…

Computer Science and Game Theory · Computer Science 2025-11-20 Xi Zheng , Xiangyu Chang , Ruoxi Jia , Yong Tan

The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A…

Computer Science and Game Theory · Computer Science 2025-08-20 Björn Filter , Ralf Möller , Özgür Lütfü Özçep

Recent advances in game informatics have enabled us to find strong strategies across a diverse range of games. However, these strategies are usually difficult for humans to interpret. On the other hand, research in Explainable Artificial…

Multiagent Systems · Computer Science 2024-03-13 Satoru Fujii

With the widespread use of sophisticated machine learning models in sensitive applications, understanding their decision-making has become an essential task. Models trained on tabular data have witnessed significant progress in explanations…

Machine Learning · Computer Science 2022-06-16 Aditya Lahiri , Kamran Alipour , Ehsan Adeli , Babak Salimi

Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes…

Machine Learning · Statistics 2025-08-19 Michael Mayer , Mario V. Wüthrich

Explainable Artificial Intelligence (XAI) has received widespread interest in recent years, and two of the most popular types of explanations are feature attributions, and counterfactual explanations. These classes of approaches have been…

Artificial Intelligence · Computer Science 2023-07-14 Emanuele Albini , Shubham Sharma , Saumitra Mishra , Danial Dervovic , Daniele Magazzeni

A large branch of explainable machine learning is grounded in cooperative game theory. However, research indicates that game-theoretic explanations may mislead or be hard to interpret. We argue that often there is a critical mismatch…

Machine Learning · Computer Science 2024-10-28 Luca Franceschi , Michele Donini , Cédric Archambeau , Matthias Seeger

Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…

Machine Learning · Computer Science 2020-02-28 Amirata Ghorbani , Michael P. Kim , James Zou

What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles,…

Machine Learning · Computer Science 2021-06-14 Benedek Rozemberczki , Rik Sarkar
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